I think that a misreading of the text takes place if one views Parris's motives to save Proctor and to get him to confess as anything other than self- interest. In the final act of the drama, Parris enters as a shell of a man that he once was. The once proud and confident leader of the church has been reduced to being fearful and completely anxious. He is aware that in other towns, the witch trials have been rebuked and those in the position of power who preside over them have been removed from their leadership positions. Parris also realizes that he has had death threats made against him, and that his position in the town is tenuous. He recognizes that he needs to do something to turn public opinion in his favor and he needs to do it quickly.
It is for this reason that Parris wants to plead with the judges. Parris understands that Proctor is a popular figure in town and if he could somehow manage to turn the public perception into his favor, using Proctor is a good way to change a conversation that is not going well for him. It is in this capacity that Parris pleads with the judges and tries to angle for Proctor to confess. A confession from Proctor is something that Parris believes will help his cause with the townspeople. Throughout the drama, Parris has been shown as one who is more worried about his power and prestige than anything else. His image is the most important element in his own mind. As a result, the recent negative perception about the witch trials don't really help him. This results in him having to pleads with the judges in order to extract a confession from Proctor.